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ON CYCLIC POLYGROUPS OF ORDER LESS THAN SIX AND PERIOD TWO

  • Kheradmand, M.R. (Department of Mathematics, Yazd University) ;
  • Davvaz, B. (Department of Mathematics, Yazd University)
  • Received : 2018.11.24
  • Accepted : 2019.09.29
  • Published : 2019.11.30

Abstract

Cyclic hypergroups are of great importance due to their applications to many field in mathematics. In this paper, we classify all polygroups of order less than six where each of its non-identity elements is a generator.

Keywords

References

  1. M. Al Tahan & B. Davvaz: On a special single-power cyclic hypergroup and its automorphisms. Discrete Mathematics, Algorithms and Applications 8 (2016), no. 4, 1650059 (12 pages).
  2. D. Comer: Polygroups derived from cogroups. J. Algebra 89 (1984), no. 2, 397-405. https://doi.org/10.1016/0021-8693(84)90225-4
  3. P. Corsini: Prolegomena of hypergroup theory. Second edition, Aviain editore, Italy, 1993.
  4. P. Corsini & V. Leoreanu: Applications of hyperstructure theory. The Netherlands, Dordrecht: Kluwer Academic Publishers (Advances in Mathematics), 2003.
  5. B. Davvaz & V. Leoreanu-Fotea: Hyperring theory and applications. International Academic Press, USA, 2007.
  6. B. Davvaz: Polygroups theory and related systems. World Scientific Publishing Co. Pte. Ltd., 2013.
  7. M. De Salvo & D. Freni: Cyclic semihypergroups and hypergroups. (Italian) Atti Sem. Mat. Fis. Univ. Modena 30 (1981), no. 1, 44-59.
  8. V. Leoreanu: About the simplifiable cyclic semihypergroups. Ital. J. Pure Appl. Math. 7 (2000), 69-76.
  9. F. Marty: Sur une generalization de la notion de groupe. In: Proceedings of the 8th Congress des Mathematiciens; Scandinavia, Stockholm, (1934), 45-49.
  10. S.Sh. Mousavi, V. Leoreanu-Fotea & M. Jafarpour: Cyclic groups obtained as quotient hypergroups. An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 61 (2015), no. 1, 109-122.
  11. T. Vougiouklis: Cyclicity in a special class of hypergroups. Acta Univ. Carolin. Math. Phys. 22 (1981), no. 1, 3-6.
  12. T. Vougiouklis: Hyperstructures and their representations. Hadronic Press, Inc, 115, Palm Harber, USA, 1994.